General Relativity and Quantum Cosmology

Title:
Harmonic Initial-Boundary Evolution in General Relativity

Abstract: Computational techniques which establish the stability of an
evolution-boundary algorithm for a model wave equation with shift are
incorporated into a well-posed version of the initial-boundary value problem
for gravitational theory in harmonic coordinates. The resulting algorithm is
implemented as a 3-dimensional numerical code which we demonstrate to provide
stable, convergent Cauchy evolution in gauge wave and shifted gauge wave
testbeds. Code performance is compared for Dirichlet, Neumann and Sommerfeld
boundary conditions and for boundary conditions which explicitly incorporate
constraint preservation. The results are used to assess strategies for
obtaining physically realistic boundary data by means of Cauchy-characteristic
matching.